13,19 8. Find the length of the curve r(t) = (21-0≤t≤1.9. The helix r₁(t)= cos ti+ sin tj + tk intersects the curver₂(t) = (1 + t)i + t2j+t³k at the point (1, 0, 0). Find theangle of intersection of these curves.siga10. Reparametrize the curve r(t) = e'i + e' sin tj + e' cost kwith respect to arc length measured from the point (1, 0, 1)in the direction of increasing t.11. For the curve given by r(t) = (sin³t, cos³t, sin²t),0 ≤t≤ π/2, find365 X 21(a) the unit tangent vector,(b) the unit normal vector, (1 1010(c) the unit binormal vector, andpont (d) the curvature. libyluonnonSTUIN 5112. Find the curvature of the ellipse x = 3 cos t, y = 4 sin tatthe points (3, 0) and (0, 4).13. Find the curvature of the curve y = x4 at the point (1, 1).14. Find an equation of the osculating circle of the curvey = x - x² at the origin. Graph both the curve and itsosculating circle.i.tlls to15. Find an equation of the osculating plane of the curvex = sin 2t, y = t, z = cos 2t at the point (0, 7, 1). 8. Find the length of the curve r(t) = (21-0≤t≤1.9. The helix r₁(t)= cos ti+ sin tj + tk intersects the curver₂(t) = (1 + t)i + t2j+t³k at the point (1, 0, 0). Find theangle of intersection of these curves.siga10. Reparametrize the curve r(t) = e'i + e' sin tj + e' cost kwith respect to arc length measured from the point (1, 0, 1)in the direction of increasing t.11. For the curve given by r(t) = (sin³t, cos³t, sin²t),0 ≤t≤ π/2, find365 X 21(a) the unit tangent vector,(b) the unit normal vector, (1 1010(c) the unit binormal vector, andpont (d) the curvature. libyluonnonSTUIN 5112. Find the curvature of the ellipse x = 3 cos t, y = 4 sin tatthe points (3, 0) and (0, 4).13. Find the curvature of the curve y = x4 at the point (1, 1).14. Find an equation of the osculating circle of the curvey = x - x² at the origin. Graph both the curve and itsosculating circle.i.tlls to15. Find an equation of the osculating plane of the curvex = sin 2t, y = t, z = cos 2t at the point (0, 7, 1).

13. Answer To find the curvature of the curve y = x^4 at the point (1,1), we need to find the radius…

13. Find the curvature of the curve y = x at the point (1, 1). 14. Find an equation of the osculating circle of the curve y = x - x² at the origin. Graph both the curve and its osculating circle. 15. Find an equation of the osculating plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, 7, 1).

13. Find the curvature of the curve y = x at the point (1, 1). 14. Find an equation of the osculating circle of the curve y = x - x² at the origin. Graph both the curve and its osculating circle. 15. Find an equation of the osculating plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, 7, 1).

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

13,19

8. Find the length of the curve r(t) = (21-
0≤t≤1.
9. The helix r₁(t)
= cos ti+ sin tj + tk intersects the curve
r₂(t) = (1 + t)i + t2j+t³k at the point (1, 0, 0). Find the
angle of intersection of these curves.
siga
10. Reparametrize the curve r(t) = e'i + e' sin tj + e' cost k
with respect to arc length measured from the point (1, 0, 1)
in the direction of increasing t.
11. For the curve given by r(t) = (sin³t, cos³t, sin²t),
0 ≤t≤ π/2, find
365 X 21
(a) the unit tangent vector,
(b) the unit normal vector, (1 1010
(c) the unit binormal vector, and
pont (d) the curvature. libyluonnon
STUIN 51
12. Find the curvature of the ellipse x = 3 cos t, y = 4 sin tat
the points (3, 0) and (0, 4).
13. Find the curvature of the curve y = x4 at the point (1, 1).
14. Find an equation of the osculating circle of the curve
y = x - x² at the origin. Graph both the curve and its
osculating circle.i.tlls to
15. Find an equation of the osculating plane of the curve
x = sin 2t, y = t, z = cos 2t at the point (0, 7, 1).

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